Abstract: Hesitant fuzzy oft sets has been widely concerned as a tool to deal with uncertainty problems.In this paper, we proposed a new concept of generalized dual hesitant fuzzy soft sets by combining the generalized hesitant fuzzy soft sets with dual hesitant fuzzy sets. The operation concept of intersection, union,complement,“and”,“or” were defined by the concept of the generalized dual hesitant fuzzy soft sets established in this paper. Meanwhile, we discuss some basic properties of the operation in detail. In addition, the concepts of information energy, correlation and correlation coefficient of the generalized dual hesitation fuzzy soft sets are defined and their properties are discussed. Finally, a multi-attribute decision making method based on the generalized dual hesitation fuzzy soft set is presented. The feasibility and effectiveness of the method are illustrated by an example.

Key words: dual hesitant fuzzy sets, generalized fuzzy soft sets, generalized dual hesitation fuzzy soft sets, correlation coefficient, multi-attribute decision making

摘要： 犹豫模糊软集作为一种处理不确定问题的工具受到了广泛关注。本文将广义模糊软集与对偶犹豫模糊集相结合,提出了广义对偶犹豫模糊软集的概念,给出了广义对偶犹豫模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,定义了广义对偶犹豫模糊软集的信息能量、相关性和相关系数的概念并讨论了它的性质。最后,给出了基于广义对偶犹豫模糊软集的多属性决策方法,并通过实例说明了该方法的的可行性和有效性。

关键词: 对偶犹豫模糊集, 广义模糊软集, 广义对偶犹豫模糊软集, 相关系数, 多属性决策